Mendel's laws

Rediscovery Mendel's laws Hugo de Vries in Holland, Karl Correns in Germany and Erich Chermak in Austria occurred only in 1900 year. At the same time, archives were opened and Mendel's old works were found.

At this time, the scientific world was already ready to accept genetics. Her triumphal march began. They checked the validity of the laws of inheritance according to Mendel (Mendelization) on more and more new plants and animals and received constant confirmation. All exceptions to the rules quickly developed into new phenomena of the general theory of heredity.

Currently, the three fundamental laws of genetics, Mendel's three laws, are formulated as follows.

Mendel's first law. Uniformity of first generation hybrids. All characteristics of an organism can be in their dominant or recessive manifestation, which depends on the alleles of a given gene present. Each organism has two alleles of each gene (2n chromosomes). For manifestation dominant allele one copy of it is enough to manifest recessive- we need two at once. So, genotypes AA And Ahh peas produce red flowers, and only the genotype ahh gives white. So when we cross red peas with white peas:

AA x aa Aa

As a result of crossing, we get all the first generation offspring with red flowers. However, not all so simple. Some genes in some organisms may not be dominant or recessive, but codominant. As a result of such crossing, for example, in petunia and cosmos, we will get the entire first generation with pink flowers - an intermediate manifestation of the red and white alleles.

Mendel's second law. Splitting of characters in the second generation in a ratio of 3:1. When heterozygous hybrids of the first generation, carrying dominant and recessive alleles, self-pollinate, in the second generation the characters are split in a ratio of 3:1.

Mendelian crosses can be shown in the following diagram:

P: AA x aa F1: Aa x Aa F2: AA + Aa + Aa + aa

That is, one F 2 plant carries a homozygous dominant genotype, two have a heterozygous genotype (but the dominant allele appears in the phenotype!), and one plant is homozygous for a recessive allele. This results in a phenotypic splitting of the trait in a ratio of 3:1, although the genotypic splitting is actually 1:2:1. In the case of a codominant trait, such a split is observed, for example, in the color of flowers in petunia: one plant with red flowers, two with pink and one with white.

Mendel's third law. Law of independent inheritance of different characteristics

For dihybrid crossing, Mendel took homozygous pea plants that differed in two genes - seed color (yellow, green) and seed shape (smooth, wrinkled). Dominant characteristics - yellow color (I) and smooth shape (R) seeds Each plant produces one variety of gametes according to the alleles studied. When gametes merge, all offspring will be uniform: II Rr.

When gametes are formed in a hybrid, from each pair of allelic genes, only one gets into the gamete, and due to the randomness of the divergence of the paternal and maternal chromosomes in the first division of meiosis, the gene I can get into the same gamete with the gene R or with a gene r. Likewise, the gene i may be in the same gamete with the gene R or with a gene r. Therefore, the hybrid produces four types of gametes: IR, Ir, iR, ir. During fertilization, each of the four types of gametes from one organism encounters randomly any of the gametes from another organism. All possible combinations of male and female gametes can be easily established using Punnett gratings, in which the gametes of one parent are written out horizontally, and the gametes of the other parent vertically. The genotypes of zygotes formed during the fusion of gametes are entered into the squares.

It is easy to calculate that according to the phenotype, the offspring are divided into 4 groups: 9 yellow smooth, 3 yellow wrinkled, 3 green smooth, 1 yellow wrinkled, that is, a splitting ratio of 9: 3: 3: 1 is observed. If we take into account the results of splitting for each pair of characters separately, it turns out that the ratio of the number of yellow seeds to the number of green ones and the ratio of smooth seeds to wrinkled ones for each pair is equal to 3:1. Thus, with a dihybrid crossing, each pair of characters, when split in the offspring, behaves in the same way as with a monohybrid crossing, i.e., independently of the other pair of characters.

During fertilization, gametes are combined according to the rules of random combinations, but with equal probability for each. In the resulting zygotes, various combinations of genes arise.

Independent distribution of genes in the offspring and the occurrence of various combinations of these genes during dihybrid crossing is possible only if pairs of allelic genes are located in different pairs of homologous chromosomes.

Thus, Mendel's third law is formulated as follows: When crossing two homozygous individuals that differ from each other in two or more pairs of alternative traits, the genes and their corresponding traits are inherited independently of each other.

Recessive flew. Mendel obtained identical numerical ratios when splitting the alleles of many pairs of traits. This in particular implied equal survival of individuals of all genotypes, but this may not be the case. It happens that a homozygote for some trait does not survive. For example, yellow coloration in mice may be due to heterozygosity for Aguti yellow. When crossing such heterozygotes with each other, one would expect segregation for this trait in a ratio of 3:1. However, a 2:1 split is observed, that is, 2 yellow to 1 white (recessive homozygote).

A y a x A y a 1aa + 2A y a + 1A y A y -- the last genotype does not survive.

It has been shown that the dominant (by color) homozygote does not survive even at the embryonic stage. This allele is simultaneously recessive lethality(that is, a recessive mutation leading to the death of the organism).

Half-flying. Mendelian segregation disorder often occurs because some genes are semi-flying-- the viability of gametes or zygotes with such alleles is reduced by 10-50%, which leads to a violation of 3:1 cleavage.

Influence of the external environment. The expression of some genes may be highly dependent on environmental conditions. For example, some alleles appear phenotypically only at a certain temperature during a certain phase of the organism's development. This can also lead to violations of Mendelian segregation.

Modifier genes and polygenes. Except main gene, which controls this trait, there may be several more in the genotype modifier genes, modifying the expression of the main gene. Some traits may be determined not by one gene, but by a whole complex of genes, each of which contributes to the manifestation of the trait. This sign is usually called polygenic. All this also disrupts the 3:1 split.

heredity hybrid crossing mendel

Mendel's third law is the law of independent distribution of characteristics. This means that each gene of one allelic pair can appear in a gamete with any other gene from another allelic pair. For example, if an organism is heterozygous for two genes under study (AaBb), then it forms the following types of gametes: AB, Ab, aB, ab. That is, for example, gene A can be in the same gamete with both gene B and b. The same applies to other genes (their arbitrary combination with non-allelic genes).

Mendel's third law is already evident with dihybrid crossing(especially with trihybrid and polyhybrid), when pure lines differ in two studied characteristics. Mendel crossed a pea variety with yellow smooth seeds with a variety that had green wrinkled seeds and obtained exclusively yellow smooth seeds F 1 . Next, he grew F 1 plants from the seeds, allowed them to self-pollinate, and obtained F 2 seeds. And here he observed splitting: plants appeared with both green and wrinkled seeds. The most surprising thing was that among the second generation hybrids there were not only plants with smooth yellow and green wrinkled seeds. There were also yellow wrinkled and green smooth seeds, i.e., recombination of characters occurred, and combinations were obtained that were not found in the original parental forms.

Analyzing the quantitative ratio of different F2 seeds, Mendel discovered the following:

If we consider each trait separately, it was split in a ratio of 3:1, as in a monohybrid cross. That is, for every three yellow seeds there was one green one, and for every 3 smooth ones there was one wrinkled one.

Plants with new combinations of traits appeared.

The phenotypic ratio was 9:3:3:1, where for every nine yellow smooth pea seeds there were three yellow wrinkled, three green smooth and one green wrinkled.

Mendel's third law is well illustrated by the Punnett lattice. Here, the possible gametes of the parents (in this case, first-generation hybrids) are written in the row and column headings. The probability of producing each type of gamete is ¼. It is also equally likely that they will combine differently into one zygote.

We see that four phenotypes are formed, two of which did not previously exist. The ratio of phenotypes is 9: 3: 3: 1. The number of different genotypes and their ratio is more complex:

This results in 9 different genotypes. Their ratio is: 4: 2: 2: 2: 2: 1: 1: 1: 1. At the same time, heterozygotes are more common, and homozygotes are less common.

If we return to the fact that each trait is inherited independently, and a 3:1 split is observed for each, then we can calculate the probability of phenotypes for two traits of different alleles by multiplying the probability of manifestation of each allele (i.e., it is not necessary to use the Punnett lattice). Thus, the probability of smooth yellow seeds will be equal to ¾ × ¾ = 9/16, smooth green – ¾ × ¼ = 3/16, wrinkled yellow – ¼ × ¾ = 3/16, wrinkled green – ¼ × ¼ = 1/16. Thus, we get the same phenotypic ratio: 9:3:3:1.

Mendel's third law is explained by the independent divergence of homologous chromosomes of different pairs during the first division of meiosis. A chromosome containing gene A can, with equal probability, go into the same cell with both a chromosome containing gene B and a chromosome containing gene b. The chromosome with gene A is in no way linked to the chromosome with gene B, although they were both inherited from the same parent. We can say that as a result of meiosis, the chromosomes are mixed. The number of their different combinations is calculated by the formula 2 n, where n is the number of chromosomes of the haploid set. So, if a species has three pairs of chromosomes, then the number of different combinations of them will be 8 (2 3).

When the law of independent inheritance of characteristics does not apply

Mendel's third law, or the law of independent inheritance of traits, applies only to genes localized on different chromosomes or located on the same chromosome, but quite far from each other.

Basically, if genes are located on the same chromosome, then they are inherited together, that is, they exhibit linkage with each other, and the law of independent inheritance of traits no longer applies.

For example, if the genes responsible for the color and shape of pea seeds were on the same chromosome, then the first generation hybrids could form gametes of only two types (AB and ab), since during meiosis the parental chromosomes diverge independently of each other, but not individual genes. In this case, in the second generation there would be a 3:1 split (three yellow smooth to one green wrinkled).

However, it's not that simple. Due to the existence in nature of conjugation (bringing together) of chromosomes and crossing over (exchange of chromosome sections), genes located on homologous chromosomes also recombine. So, if a chromosome with the AB genes, during the process of crossing over, exchanges a section with the B gene with a homologous chromosome, whose section contains the b gene, then new gametes (Ab and, for example, aB) can be obtained. The percentage of such recombinant gametes will be less than if the genes were on different chromosomes. In this case, the probability of crossing over depends on the distance of genes on the chromosome: the further away, the greater the probability.

The improvement of the hybridiological method allowed G. Mendel to identify a number of the most important patterns of inheritance of traits in peas, which, as it later turned out, are true for all diploid organisms that reproduce sexually.

When describing the results of crossings, Mendel himself did not interpret the facts he established as certain laws. But after their rediscovery and confirmation on plant and animal objects, these phenomena, repeated under certain conditions, began to be called the laws of inheritance of characteristics in hybrids.

Some researchers distinguish not three, but two of Mendel's laws. At the same time, some scientists combine the first and second laws, believing that the first law is part of the second and describes the genotypes and phenotypes of the descendants of the first generation (F1). Other researchers combine the second and third laws into one, believing that the “law of independent combination” is in essence the “law of independence of segregation” that occurs simultaneously in different pairs of alleles. However, in Russian literature we are talking about Mendel’s three laws.

Mendel's great scientific success was that the seven traits he chose were determined by genes on different chromosomes, which excluded possible linked inheritance. He found that:

1) In first-generation hybrids, the trait of only one parental form is present, while the other “disappears.” This is the law of uniformity of first generation hybrids.

2) In the second generation, a split is observed: three quarters of the descendants have the trait of hybrids of the first generation, and a quarter have a trait that “disappeared” in the first generation. This is the law of splitting.

3) Each pair of traits is inherited independently of the other pair. This is the law of independent inheritance.

Of course, Mendel did not know that these provisions would eventually be called Mendel's first, second and third laws.

Modern wording of laws

Mendel's first law

The law of uniformity of first-generation hybrids - when crossing two homozygous organisms belonging to different pure lines and differing from each other in one pair of alternative manifestations of a trait, the entire first generation of hybrids (F1) will be uniform and will carry a manifestation of the trait of one of the parents.

This law is also known as the "law of trait dominance." Its formulation is based on the concept of a pure line relative to the trait being studied - in modern language this means homozygosity of individuals for this trait.

Mendel's second law

The law of segregation - when two heterozygous descendants of the first generation are crossed with each other in the second generation, segregation is observed in a certain numerical ratio: by phenotype 3:1, by genotype 1:2:1.

The phenomenon in which the crossing of heterozygous individuals leads to the formation of offspring, some of which carry a dominant trait, and some - a recessive one, is called segregation. Consequently, splitting is the distribution (recombination) of dominant and recessive traits among the offspring in a certain numerical ratio. The recessive trait does not disappear in the first generation hybrids, but is only suppressed and appears in the second hybrid generation.

The splitting of offspring when crossing heterozygous individuals is explained by the fact that the gametes are genetically pure, that is, they carry only one gene from an allelic pair. The law of gamete purity can be formulated as follows: during the formation of germ cells, only one allele from a pair of alleles of a given gene enters each gamete. The cytological basis for the splitting of characters is the divergence of homologous chromosomes and the formation of haploid germ cells in meiosis (Fig. 4).

Fig.4.

The example illustrates crossing plants with smooth and wrinkled seeds. Only two pairs of chromosomes are depicted; one of these pairs contains the gene responsible for the shape of the seeds. In plants with smooth seeds, meiosis leads to the formation of gametes with the smooth allele (R), and in plants with wrinkled seeds, gametes with the wrinkled allele (r). First generation F1 hybrids have one chromosome with the smooth allele and one chromosome with the wrinkled allele. Meiosis in F1 leads to the formation of equal numbers of gametes with R and with r. The random pairwise combination of these gametes during fertilization leads in the F2 generation to the appearance of individuals with smooth and wrinkled peas in a ratio of 3:1.

Mendel's third law

The law of independent inheritance - when crossing two individuals that differ from each other in two (or more) pairs of alternative traits, genes and their corresponding traits are inherited independently of each other and are combined in all possible combinations (as in monohybrid crossing).

Mendeleev's law of independent inheritance can be explained by the movement of chromosomes during meiosis (Fig. 5). During the formation of gametes, the distribution of alleles from a given pair of homologous chromosomes between them occurs independently of the distribution of alleles from other pairs. It is the random arrangement of homologous chromosomes at the spindle equator in metaphase I of meiosis and their subsequent arrangement in anaphase I that leads to a variety of recombinations of alleles in gametes. The number of possible combinations of alleles in male or female gametes can be determined by the general formula 2n, where n is the haploid number of chromosomes. In humans, n=23, and the possible number of different combinations is 223=8,388,608.

Fig.5. Explanation of the Mendelian law of independent distribution of factors (alleles) R, r, Y, y as a result of the independent divergence of different pairs of homologous chromosomes in meiosis. Crossing plants that differ in the shape and color of seeds (smooth yellow and green wrinkled) produces hybrid plants in which the chromosomes of one homologous pair contain the R and r alleles, and the other homologous pair contains the Y and y alleles. In metaphase I of meiosis, chromosomes obtained from each parent can with equal probability go either to the same spindle pole (left picture) or to different ones (right picture). In the first case, gametes arise containing the same combinations of genes (YR and yr) as in the parents, in the second case - alternative combinations of genes (Yr and yR). As a result, with a probability of 1/4, four types of gametes are formed; a random combination of these types leads to the splitting of the offspring 9: 3: 3: 1, as was observed by Mendel.

Crossing:

1. Monohybrid. Observation is carried out only according to one sign, i.e. alleles of one gene are tracked.
2. Dihybrid. Observation is carried out according to two characteristics, that is, the alleles of two genes are tracked.

Genetic designations:

P – parents; F – offspring, the number indicates the serial number of the generation, F1, F2.

X – crossing icon, males, females; A, a, B, c, C, c are individual hereditary characteristics. A, B, C are dominant alleles of the gene, and, b, c are recessive alleles of the gene. Aa – , heterozygote; aa is a recessive homozygote, AA is a dominant homozygote.

Monohybrid crossing.

A classic example of a monohybrid cross is the crossing of varieties with yellow and green seeds: all descendants had yellow seeds. Mendel came to the conclusion that in a first-generation hybrid, of each pair of alternative characters, only one - dominant - appears, and the second - recessive - does not develop, as if disappears.

R AA * aa – parents (pure lines)

Ah, ah - parents

Aa – first generation of hybrids

This pattern was called the law of uniformity of first-generation hybrids or the law of dominance. This is Mendel's first law: when crossing two organisms belonging to different pure lines (two organisms), differing from each other in one pair of alternative traits, the entire first generation of hybrids (F1) will be uniform and will carry the trait of one of the parents.

Mendel's second law

The seeds of the first generation hybrids were used by Mendel to obtain the second generation. When crossing, the characteristics are split in a certain numerical ratio. Some hybrids carry a dominant trait, while others carry a recessive trait.

F1 Aa * Aa A, a, A, a F2 AA (0.25); Aa (0.25); Aa (0.25); aa (0.25)

In the offspring, traits are split in a 3:1 ratio.

To explain the phenomena of dominance and segregation, Mendel proposed the hypothesis of gamete purity: hereditary factors do not mix during the formation of hybrids, but are preserved unchanged.

Mendel's second law can be formulated: when two descendants of the first generation are crossed with each other (two heterozygous individuals), in the second generation a split is observed in a certain numerical ratio: by phenotype 3:1, by - 1:2:1.

Mendel's third law: during dihybrid crossing in second-generation hybrids, each pair of contrasting characters is inherited independently of the others and gives different combinations with them. The law is valid only in cases where the analyzed features are not linked to each other, i.e. are located on non-homologous chromosomes.

Consider Mendel's experiment in which he studied the independent inheritance of traits in peas. One of the plants crossed had smooth, yellow seeds, while the other had wrinkled and green seeds. In the first generation of hybrids, the plants had smooth and yellow seeds. In the second generation, cleavage occurred according to the 9:3:3:1 phenotype.

Mendel's third law is formulated as follows: splitting for each pair of genes occurs independently of other pairs of genes.

Gregor Mendel is an Austrian botanist who studied and described Mendel's Laws - which to this day play an important role in the study of the influence of heredity and the transmission of hereditary traits.

In his experiments, the scientist crossed different types of peas that differed in one alternative trait: color of flowers, smooth-wrinkled peas, stem height. In addition, a distinctive feature of Mendel’s experiments was the use of so-called “pure lines”, i.e. offspring resulting from self-pollination of the parent plant. Mendel's laws, formulation and brief description will be discussed below.

Having studied and meticulously prepared an experiment with peas for many years: using special bags to protect the flowers from external pollination, the Austrian scientist achieved incredible results at that time. A thorough and lengthy analysis of the data obtained allowed the researcher to deduce the laws of heredity, which were later called “Mendel’s Laws.”

Before we begin to describe the laws, we should introduce several concepts necessary for understanding this text:

Dominant gene- a gene whose trait is manifested in the body. Designated A, B. When crossed, such a trait is considered conditionally stronger, i.e. it will always appear if the second parent plant has conditionally weaker characteristics. This is what Mendel's laws prove.

Recessive gene - the gene is not expressed in the phenotype, although it is present in the genotype. Denoted by the capital letter a,b.

Heterozygous - a hybrid whose genotype (set of genes) contains both a dominant and a certain trait. (Aa or Bb)

Homozygous - hybrid , possessing exclusively dominant or only recessive genes responsible for a certain trait. (AA or bb)

Mendel's Laws, briefly formulated, will be discussed below.

Mendel's first law, also known as the law of hybrid uniformity, can be formulated as follows: the first generation of hybrids resulting from crossing pure lines of paternal and maternal plants has no phenotypic (i.e. external) differences in the trait being studied. In other words, all daughter plants have the same color of flowers, stem height, smoothness or roughness of peas. Moreover, the manifested trait phenotypically exactly corresponds to the original trait of one of the parents.

Mendel's second law or the law of segregation states: the offspring of heterozygous hybrids of the first generation during self-pollination or inbreeding have both recessive and dominant characters. Moreover, splitting occurs according to the following principle: 75% are plants with a dominant trait, the remaining 25% are with a recessive trait. Simply put, if the parent plants had red flowers (dominant trait) and yellow flowers (recessive trait), then the daughter plants will have 3/4 red flowers and the rest yellow.

Third And last Mendel's law, which is also called in general terms, means the following: when crossing homozygous plants possessing 2 or more different characteristics (that is, for example, a tall plant with red flowers (AABB) and a short plant with yellow flowers (aabb), the characteristics studied (stem height and color of flowers) are inherited independently. In other words, the result of crossing can be tall plants with yellow flowers (Aabb) or short ones with red flowers (aaBb).

Mendel's laws, discovered in the mid-19th century, gained recognition much later. On their basis, all modern genetics was built, and after it, selection. In addition, Mendel's laws confirm the great diversity of species that exist today.